Finite Group Databasebeta

← #15769429

Subgroups — #15769429

Order 3328.

1578 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88200C211yesmaximal, characteristic
2C22×#88075C211yesmaximal, characteristic, complemented
3C22×#88060C211yesmaximal, characteristic
4C2×#11718648C211yesmaximal, characteristic
5C2×#11718143C211yesmaximal, characteristic, complemented
6C2×#11718121C211yesmaximal, characteristic, complemented
7C22×C13×#103C211yesmaximal, characteristic, complemented
8C23×Q8×C13C2211yescharacteristic
9C23×C4×D13C2211yescharacteristic
10C23×C8×C13C2211yescharacteristic
11C22×C13×C4⋊C4C2211yescharacteristic
12C2×#88200—22no—
13C2×#88200—22no—
14C2×#88200—22no—
15C2×#88200—22no—
16C2×#88200—22no—
17C2×#88200C414yescomplemented
18C22×#6103—21no—
19C22×#6103—21no—
20C22×C4⋊Dic13C2211yescharacteristic
21C22×C4⋊Dic13C2211yescharacteristic
22C22×#6101—21no—
23C23×#1055C2211yescharacteristic
24C2×C13×#103—22no—
25C2×C13×#103—22no—
26C2×C13×#103—22no—
27C2×#88075—22no—
28C2×#88075—22no—
29C2×#88075—22no—
30C2×#88071—21no—
31C2×#88060—22no—
32C2×#88060—22no—
33C2×#88060—22no—
34#11718648—22no—
35#11718648—22no—
36#11718143—22no—
37#11718121—22no—
38C24×D13D411yescharacteristic
39C22×Q8×C13—21no—
40C22×Q8×C13—21no—
41C22×Q8×C13—21no—
42C22×Q8×C13—21no—
43C22×Q8×C13—21no—
44C22×Q8×C13—21no—
45C22×Q8×C13—21no—
46C22×Q8×C13—21no—
47C22×Q8×C13—21no—
48C22×Q8×C13—21no—
49C22×Q8×C13—21no—
50C22×Q8×C13C2×C412yes—
51C22×Q8×C13D412yes—
52C22×Q8×C13D412yes—
53C23×C4×C13—21no—
54C23×C4×C13—21no—
55C23×C4×C13C2311yescharacteristic
56C23×Dic13—21no—
57C23×Dic13—21no—
58C23×Dic13D411yescharacteristic
59C22×C4×D13—21no—
60C22×C4×D13—21no—
61C22×C4×D13—21no—
62C22×C4×D13—21no—
63C22×C4×D13—21no—
64C22×C4×D13—21no—
65C22×C4×D13—21no—
66C22×C4×D13—21no—
67C22×C4×D13—21no—
68C22×C4×D13—21no—
69C22×C4×D13—21no—
70C22×C4×D13—21no—
71C22×C4×D13C2×C412yes—
72C22×C4×D13D412yes—
73C22×C8×C13—21no—
74C22×C8×C13—21no—
75C22×C8×C13—21no—
76C22×C8×C13—21no—
77C22×C8×C13—21no—
78C22×C8×C13—21no—
79C22×C8×C13D412yes—
80C2×C13×C4⋊C4—21no—
81C2×C13×C4⋊C4—21no—
82C2×C13×C4⋊C4—21no—
83C2×C13×C4⋊C4—21no—
84C2×C13×C4⋊C4—21no—
85C2×C13×C4⋊C4D412yes—
86#88200—28no—
87#88200—28no—
88#88200—28no—
89#88200—28no—
90C2×#6103—24no—
91C2×#6103—24no—
92C2×#6103—24no—
93C2×#6103—24no—
94C2×#6103—42no—
95C2×#6103—42no—
96C2×C4⋊Dic13—21no—
97C2×C4⋊Dic13—21no—
98C2×C4⋊Dic13—21no—
99C2×C4⋊Dic13—21no—
100C2×C4⋊Dic13—21no—
101C2×C4⋊Dic13—21no—
102C2×C4⋊Dic13—21no—
103C2×C4⋊Dic13—21no—
104C2×C4⋊Dic13C2×C412yes—
105C2×C4⋊Dic13D412yes—
106C2×C4⋊Dic13D412yes—
107C2×C4⋊Dic13D412yes—
108C2×#6101—24no—
109C2×#6101—24no—
110C2×#6101—24no—
111C22×#1055—21no—
112C22×#1055—21no—
113C22×#1055—21no—
114C22×#1055—21no—
115C22×#1055—21no—
116C22×#1055—21no—
117C22×#1055D412yes—
118C13×#103—28no—
119#88075—28no—
120#88071—24no—
121#88060—28no—
122#10970—131nomaximal, Sylow
123C24×C13C2×D411yescharacteristic
124C23×D13—21no—
125C23×D13—21no—
126C23×D13—21no—
127C23×D13—21no—
128C23×D13—21no—
129C23×D13—21no—
130C23×D13—21no—
131C23×D13—21no—
132C23×D13—21no—
133C23×D13—21no—
134C23×D13—21no—
135C23×D13—21no—
136C23×D13C22⋊C412yes—
137C23×D13SD1612yes—
138C23×D13Q1612yes—
139C2×Q8×C13—22no—
140C2×Q8×C13—22no—
141C2×Q8×C13—22no—
142C2×Q8×C13—22no—
143C2×Q8×C13—22no—
144C2×Q8×C13—22no—
145C2×Q8×C13—22no—
146C2×Q8×C13—22no—
147C2×Q8×C13—22no—
148C2×Q8×C13—22no—
149C2×Q8×C13—22no—
150C2×Q8×C13—22no—
151C2×Q8×C13—22no—
152C2×Q8×C13—22no—
153C2×Q8×C13—22no—
154C2×Q8×C13—41no—
155C2×Q8×C13—41no—
156C2×Q8×C13—41no—
157C2×Q8×C13—41no—
158C2×Q8×C13—41no—
159C2×Q8×C13—41no—
160C2×Q8×C13—41no—
161C2×Q8×C13—41no—
162C2×Q8×C13—41no—
163C2×Q8×C13—41no—
164C2×Q8×C13—41no—
165C2×Q8×C13—41no—
166C2×Q8×C13C22⋊C414yescomplemented
167C22×C4×C13—22no—
168C22×C4×C13—22no—
169C22×C4×C13—22no—
170C22×C4×C13—22no—
171C22×C4×C13—41no—
172C22×C4×C13—41no—
173C22×C4×C13—41no—
174C22×C4×C13—41no—
175C22×C4×C13—41no—
176C22×C4×C13—41no—
177C22×C4×C13—41no—
178C22×C4×C13—41no—
179C22×C4×C13—41no—
180C22×C4×C13—41no—
181C22×C4×C13C22×C411yescharacteristic
182C22×C4×C13C2×D411yescharacteristic
183C22×C4×C13C2×D411yescharacteristic
184C22×C4×C13C2×D411yescharacteristic
185C22×C4×C13C2×D411yescharacteristic
186C22×C4×C13C2×D411yescharacteristic
187C22×C4×C13C2×D411yescharacteristic
188C22×C4×C13C2×D411yescharacteristic
189C22×C4×C13C2×D411yescharacteristic
190C22×C4×C13C2×D411yescharacteristic
191C22×C4×C13#4111yescharacteristic
192C22×C4×C13#4111yescharacteristic
193C22×C4×C13#4111yescharacteristic
194C22×C4×C13#4111yescharacteristic
195C22×Dic13—22no—
196C22×Dic13—21no—
197C22×Dic13—21no—
198C22×Dic13—21no—
199C22×Dic13—22no—
200C22×Dic13—22no—
201C22×Dic13—21no—
202C22×Dic13—21no—
203C22×Dic13—21no—
204C22×Dic13—22no—
205C22×Dic13—41no—
206C22×Dic13—41no—
207C22×Dic13—41no—
208C22×Dic13—41no—
209C22×Dic13—41no—
210C22×Dic13—41no—
211C22×Dic13—41no—
212C22×Dic13—41no—
213C22×Dic13—41no—
214C22×Dic13—41no—
215C22×Dic13C22⋊C412yes—
216C2×C4×D13—22no—
217C2×C4×D13—22no—
218C2×C4×D13—22no—
219C2×C4×D13—22no—
220C2×C4×D13—22no—
221C2×C4×D13—22no—
222C2×C4×D13—22no—
223C2×C4×D13—22no—
224C2×C4×D13—22no—
225C2×C4×D13—22no—
226C2×C4×D13—22no—
227C2×C4×D13—22no—
228C2×C4×D13—41no—
229C2×C4×D13—41no—
230C2×C4×D13—41no—
231C2×C4×D13—41no—
232C2×C4×D13—41no—
233C2×C4×D13—41no—
234C2×C4×D13—41no—
235C2×C4×D13—41no—
236C2×C4×D13—41no—
237C2×C4×D13—41no—
238C2×C4×D13—41no—
239C2×C4×D13—41no—
240C2×C4×D13—41no—
241C2×C4×D13—41no—
242C2×C4×D13—41no—
243C2×C4×D13—41no—
244C2×C8×C13—22no—
245C2×C8×C13—22no—
246C2×C8×C13—22no—
247C2×C8×C13—41no—
248C2×C8×C13—41no—
249C2×C8×C13—41no—
250C2×C8×C13—41no—
251C13×C4⋊C4—22no—
252C13×C4⋊C4—22no—
253C13×C4⋊C4—41no—
254C13×C4⋊C4—41no—
255#6103—216no—
256#6103—48no—
257C4⋊Dic13—22no—
258C4⋊Dic13—22no—
259C4⋊Dic13—22no—
260C4⋊Dic13—22no—
261C4⋊Dic13—22no—
262C4⋊Dic13—41no—
263C4⋊Dic13—41no—
264C4⋊Dic13C22⋊C414yescomplemented
265#6101—216no—
266C2×#1055—22no—
267C2×#1055—22no—
268C2×#1055—22no—
269C2×#1055—41no—
270C2×#1055—41no—
271C2×#1055—41no—
272C2×#1055—41no—
273C22×C22⋊Q8—131no—
274C22×#103—131no—
275C22×#103D1311yescharacteristic, complemented
276C22×C22⋊C8—131no—
277C2×#380—131no—
278C2×#340—131no—
279C2×#340—131no—
280C23×C13C2×C22⋊C411yescharacteristic
281C23×C13#12011yescharacteristic
282C23×C13#12011yescharacteristic
283C23×C13#12011yescharacteristic
284C23×C13#12111yescharacteristic
285C23×C13#12111yescharacteristic
286C23×C13#12311yescharacteristic
287C23×C13C2×SD1611yescharacteristic
288C23×C13C2×Q1611yescharacteristic
289C23×C13#13511yescharacteristic
290C23×C13#13511yescharacteristic
291C23×C13AGL(1,ℤ/8)11yescharacteristic
292C23×C13#13711yescharacteristic
293C23×C13#13711yescharacteristic
294C23×C13#13711yescharacteristic
295C22×D13—22no—
296C22×D13—22no—
297C22×D13—22no—
298C22×D13—22no—
299C22×D13—22no—
300C22×D13—22no—
301C22×D13—22no—
302C22×D13—22no—
303C22×D13—22no—
304C22×D13—22no—
305C22×D13—22no—
306C22×D13—22no—
307C22×D13—22no—
308C22×D13—22no—
309C22×D13—22no—
310C22×D13—22no—
311C22×D13—22no—
312C22×D13—22no—
313C22×D13—41no—
314C22×D13—41no—
315C22×D13—41no—
316C22×D13—41no—
317C22×D13—41no—
318C22×D13—41no—
319C22×D13—41no—
320C22×D13—41no—
321C22×D13—41no—
322C22×D13—41no—
323C22×D13—41no—
324C22×D13—41no—
325C22×D13—41no—
326C22×D13—41no—
327C22×D13—41no—
328C22×D13—41no—
329C22×D13#10314yescomplemented
330Q8×C13—24no—
331Q8×C13—24no—
332Q8×C13—42no—
333Q8×C13—42no—
334Q8×C13—42no—
335Q8×C13—42no—
336Q8×C13—42no—
337Q8×C13—42no—
338C2×C4×C13—24no—
339C2×C4×C13—42no—
340C2×C4×C13—42no—
341C2×C4×C13—42no—
342C2×C4×C13—42no—
343C2×C4×C13—42no—
344C2×C4×C13—42no—
345C2×C4×C13—42no—
346C2×C4×C13—42no—
347C2×C4×C13—42no—
348C2×C4×C13—81no—
349C2×C4×C13—81no—
350C2×C4×C13—81no—
351C2×C4×C13—81no—
352C2×C4×C13C2×C22⋊C411yescharacteristic
353C2×C4×C13C2×C22⋊C411yescharacteristic
354C2×C4×C13C4×D411yescharacteristic
355C2×C4×C13C4×D411yescharacteristic
356C2×C4×C13C4×D411yescharacteristic
357C2×C4×C13C4×D411yescharacteristic
358C2×C4×C13#12011yescharacteristic
359C2×C4×C13#12011yescharacteristic
360C2×C4×C13#12011yescharacteristic
361C2×C4×C13#12011yescharacteristic
362C2×C4×C13#12011yescharacteristic
363C2×C4×C13#12111yescharacteristic
364C2×C4×C13#12111yescharacteristic
365C2×C4×C13#12111yescharacteristic
366C2×C4×C13#12111yescharacteristic
367C2×C4×C13#12111yescharacteristic
368C2×C4×C13#12111yescharacteristic
369C2×C4×C13#12111yescharacteristic
370C2×C4×C13#12111yescharacteristic
371C2×C4×C13#12111yescharacteristic
372C2×C4×C13#12111yescharacteristic
373C2×C4×C13#12311yescharacteristic
374C2×C4×C13#12311yescharacteristic
375C2×C4×C13#12311yescharacteristic
376C2×C4×C13#12411yescharacteristic
377C2×C4×C13#12411yescharacteristic
378C2×C4×C13#12711yescharacteristic
379C2×C4×C13#12711yescharacteristic
380C2×Dic13—22no—
381C2×Dic13—24no—
382C2×Dic13—22no—
383C2×Dic13—22no—
384C2×Dic13—41no—
385C2×Dic13—41no—
386C2×Dic13—41no—
387C2×Dic13—41no—
388C2×Dic13—42no—
389C2×Dic13—42no—
390C2×Dic13—42no—
391C2×Dic13—42no—
392C2×Dic13—42no—
393C2×Dic13—42no—
394C2×Dic13—42no—
395C2×Dic13—42no—
396C2×Dic13—42no—
397C2×Dic13—81no—
398C2×Dic13—81no—
399C2×Dic13—81no—
400C2×Dic13—81no—
401C4×D13—42no—
402C4×D13—42no—
403C4×D13—42no—
404C4×D13—42no—
405C4×D13—42no—
406C4×D13—42no—
407C4×D13—42no—
408C4×D13—42no—
409C8×C13—42no—
410#1055—42no—
411C23×Q8C2×D1311yescharacteristic
412C24×C4—131no—
413C23×C8—131no—
414C23×C8C2×D1311yescharacteristic
415C2×C22⋊Q8—134no—
416C2×C22⋊Q8—262no—
417C2×C22⋊Q8—262no—
418C2×C22⋊Q8—262no—
419C2×C22⋊Q8—262no—
420C2×C22⋊Q8—262no—
421C22×C4⋊C4—131no—
422C22×C4⋊C4—131no—
423C22×C4⋊C4—261no—
424C22×C4⋊C4C2×D1311yescharacteristic
425C22×C22⋊C4—261no—
426C22×C22⋊C4—261no—
427C2×#103—22no—
428C2×#103—22no—
429C2×#103—22no—
430C2×#103—262no—
431C2×#103—262no—
432C2×#103—262no—
433C2×C22⋊C8—262no—
434C2×C22⋊C8—262no—
435C2×C22⋊C8—262no—
436#380—262no—
437#380—262no—
438C2×#95—261no—
439#340—262no—
440#340—262no—
441C22×C13#37911yescharacteristic
442C22×C13#38611yescharacteristic
443C22×C13#38611yescharacteristic
444C22×C13#39211yescharacteristic
445C22×C13#39211yescharacteristic
446C22×C13#39411yescharacteristic
447C22×C13#39411yescharacteristic
448C22×C13C2×#10311yescharacteristic
449C22×C13#41611yescharacteristic
450C22×C13#41711yescharacteristic
451C22×C13#41911yescharacteristic
452C22×C13#44811yescharacteristic
453C22×C13#44811yescharacteristic
454C22×C13#44911yescharacteristic
455C22×C13#44911yescharacteristic
456C22×C13#45011yescharacteristic
457C22×C13#45111yescharacteristic
458C22×C13#45111yescharacteristic
459C22×C13#45111yescharacteristic
460C22×C13#45211yescharacteristic
461C22×C13#45211yescharacteristic
462C22×C13#45211yescharacteristic
463C22×C13#45211yescharacteristic
464C22×C13#46511yescharacteristic
465C22×C13#46511yescharacteristic
466C22×C13#46711yescharacteristic
467C22×C13#46711yescharacteristic
468C22×C13#46811yescharacteristic
469C22×C13#46811yescharacteristic
470C22×C13#47011yescharacteristic
471C22×C13#47011yescharacteristic
472C22×C13#48311yescharacteristic
473C22×C13#48411yescharacteristic
474C22×C13#48511yescharacteristic
475C22×C13#48511yescharacteristic
476C2×D13—24no—
477C2×D13—24no—
478C2×D13—24no—
479C2×D13—42no—
480C2×D13—42no—
481C2×D13—42no—
482C2×D13—42no—
483C2×D13—42no—
484C2×D13—42no—
485C2×D13—42no—
486C2×D13—42no—
487C2×D13—42no—
488C2×D13—42no—
489C2×D13—42no—
490C2×D13—42no—
491C4×C13—44no—
492C4×C13—82no—
493C4×C13#38611yescharacteristic
494C4×C13#38611yescharacteristic
495C4×C13#39011yescharacteristic
496C4×C13#39011yescharacteristic
497C4×C13#39211yescharacteristic
498C4×C13#39211yescharacteristic
499C4×C13#39411yescharacteristic
500C4×C13#39411yescharacteristic
501Dic13—42no—
502Dic13—44no—
503Dic13—82no—
504C25—131no—
505C22×Q8—21no—
506C22×Q8—21no—
507C22×Q8—21no—
508C22×Q8—21no—
509C22×Q8—21no—
510C22×Q8—21no—
511C22×Q8—21no—
512C22×Q8—21no—
513C22×Q8—21no—
514C22×Q8—21no—
515C22×Q8—21no—
516C22×Q8C4×D1312yes—
517C22×Q8D5212yes—
518C22×Q8C22⋊D1312yes—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—131no—
522C23×C4—132no—
523C23×C4—132no—
524C23×C4—261no—
525C23×C4—261no—
526C23×C4—261no—
527C23×C4—261no—
528C23×C4—261no—
529C23×C4—261no—
530C23×C4—261no—
531C23×C4—261no—
532C23×C4—261no—
533C23×C4—261no—
534C23×C4—261no—
535C23×C4—261no—
536C23×C4—261no—
537C23×C4—261no—
538C23×C4C22×D1311yescharacteristic
539C22×C8—21no—
540C22×C8—21no—
541C22×C8—21no—
542C22×C8—21no—
543C22×C8—21no—
544C22×C8—21no—
545C22×C8—132no—
546C22×C8—261no—
547C22×C8—261no—
548C22×C8—261no—
549C22×C8—261no—
550C22×C8—261no—
551C22×C8—261no—
552C22×C8C22⋊D1312yes—
553C22⋊Q8—268no—
554C22⋊Q8—268no—
555C22⋊Q8—268no—
556C22⋊Q8—268no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—132no—
563C2×C4⋊C4—132no—
564C2×C4⋊C4—132no—
565C2×C4⋊C4—132no—
566C2×C4⋊C4—264no—
567C2×C4⋊C4—264no—
568C2×C4⋊C4—264no—
569C2×C4⋊C4—261no—
570C2×C4⋊C4—261no—
571C2×C4⋊C4—261no—
572C2×C4⋊C4—261no—
573C2×C4⋊C4—261no—
574C2×C4⋊C4—261no—
575C2×C4⋊C4—261no—
576C2×C4⋊C4—261no—
577C2×C4⋊C4C22⋊D1312yes—
578C2×C22⋊C4—264no—
579C2×C22⋊C4—264no—
580C2×C22⋊C4—264no—
581C2×C22⋊C4—264no—
582C2×C22⋊C4—522no—
583C2×C22⋊C4—522no—
584#103—28no—
585#103—268no—
586C22⋊C8—268no—
587#95—264no—
588C2×C13#143811yescharacteristic
589C2×C13#178711yescharacteristic
590C2×C13#178811yescharacteristic
591C2×C13#187211yescharacteristic
592C2×C13#187311yescharacteristic
593C2×C13#189211yescharacteristic
594C2×C13#189411yescharacteristic
595C2×C13#200011yescharacteristic
596C2×C13#200011yescharacteristic
597C2×C13#200111yescharacteristic
598C2×C13#200111yescharacteristic
599C2×C13#203511yescharacteristic
600C2×C13#203511yescharacteristic
601C2×C13#203611yescharacteristic
602C2×C13#203611yescharacteristic
603D13—44no—
604C24—132no—
605C24—132no—
606C24—132no—
607C24—261no—
608C24—261no—
609C24—261no—
610C24—261no—
611C24—261no—
612C24—261no—
613C24—261no—
614C24—261no—
615C24—261no—
616C24—261no—
617C24—261no—
618C24—261no—
619C24D4×D1311yescharacteristic
620C2×Q8—22no—
621C2×Q8—22no—
622C2×Q8—22no—
623C2×Q8—22no—
624C2×Q8—22no—
625C2×Q8—22no—
626C2×Q8—22no—
627C2×Q8—22no—
628C2×Q8—22no—
629C2×Q8—22no—
630C2×Q8—22no—
631C2×Q8—22no—
632C2×Q8—22no—
633C2×Q8—22no—
634C2×Q8—22no—
635C2×Q8—41no—
636C2×Q8—41no—
637C2×Q8—41no—
638C2×Q8—41no—
639C2×Q8—41no—
640C2×Q8—41no—
641C2×Q8—41no—
642C2×Q8—41no—
643C2×Q8—41no—
644C2×Q8—41no—
645C2×Q8—41no—
646C2×Q8—41no—
647C2×Q8#610314yescomplemented
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—41no—
653C22×C4—41no—
654C22×C4—41no—
655C22×C4—41no—
656C22×C4—41no—
657C22×C4—41no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4—41no—
661C22×C4—41no—
662C22×C4—132no—
663C22×C4—262no—
664C22×C4—262no—
665C22×C4—261no—
666C22×C4—261no—
667C22×C4—261no—
668C22×C4—261no—
669C22×C4—262no—
670C22×C4—261no—
671C22×C4—261no—
672C22×C4—262no—
673C22×C4—262no—
674C22×C4—262no—
675C22×C4—262no—
676C22×C4—262no—
677C22×C4—262no—
678C22×C4—262no—
679C22×C4—262no—
680C22×C4—262no—
681C22×C4—262no—
682C22×C4—262no—
683C22×C4—262no—
684C22×C4—262no—
685C22×C4—521no—
686C22×C4—521no—
687C22×C4—521no—
688C22×C4—521no—
689C22×C4—521no—
690C22×C4—521no—
691C22×C4—521no—
692C22×C4—521no—
693C22×C4—521no—
694C22×C4—521no—
695C22×C4—521no—
696C22×C4—521no—
697C22×C4—521no—
698C22×C4—521no—
699C22×C4—521no—
700C22×C4—521no—
701C22×C4—521no—
702C22×C4—521no—
703C22×C4—521no—
704C22×C4—521no—
705C22×C4—521no—
706C22×C4—521no—
707C22×C4—521no—
708C22×C4—521no—
709C22×C4—521no—
710C22×C4—521no—
711C22×C4C2×C4×D1311yescharacteristic
712C22×C4C2×D5211yescharacteristic
713C22×C4#612711yescharacteristic
714C22×C4#612711yescharacteristic
715C22×C4D4×D1311yescharacteristic
716C22×C4D4×D1311yescharacteristic
717C22×C4D4×D1311yescharacteristic
718C22×C4D4×D1311yescharacteristic
719C22×C4D4×D1311yescharacteristic
720C22×C4#612911yescharacteristic
721C22×C4#612911yescharacteristic
722C22×C4C2×C22⋊D1311yescharacteristic
723C22×C4C2×C22⋊D1311yescharacteristic
724C22×C4C2×C22⋊D1311yescharacteristic
725C2×C8—22no—
726C2×C8—22no—
727C2×C8—22no—
728C2×C8—41no—
729C2×C8—41no—
730C2×C8—41no—
731C2×C8—41no—
732C2×C8—262no—
733C2×C8—262no—
734C2×C8—262no—
735C2×C8—521no—
736C2×C8—521no—
737C2×C8—521no—
738C2×C8—521no—
739C4⋊C4—22no—
740C4⋊C4—22no—
741C4⋊C4—41no—
742C4⋊C4—41no—
743C4⋊C4—134no—
744C4⋊C4—2616no—
745C4⋊C4—262no—
746C4⋊C4—262no—
747C4⋊C4—262no—
748C4⋊C4—262no—
749C4⋊C4—262no—
750C4⋊C4—521no—
751C4⋊C4—521no—
752C22⋊C4—2616no—
753C22⋊C4—528no—
754C13#1097011yescharacteristic, complemented, Sylow
755C23—134no—
756C23—262no—
757C23—262no—
758C23—262no—
759C23—262no—
760C23—262no—
761C23—262no—
762C23—262no—
763C23—262no—
764C23—262no—
765C23—262no—
766C23—262no—
767C23—262no—
768C23—262no—
769C23—262no—
770C23—262no—
771C23—262no—
772C23—262no—
773C23—262no—
774C23—521no—
775C23—521no—
776C23—521no—
777C23—521no—
778C23—521no—
779C23—521no—
780C23—521no—
781C23—521no—
782C23—521no—
783C23—521no—
784C23—521no—
785C23—521no—
786C23—521no—
787C23—521no—
788C23—521no—
789C23—521no—
790C23C22⋊C4×D1311yescharacteristic
791C23#8813611yescharacteristic
792C23#8813711yescharacteristic
793C23#8813811yescharacteristic
794C23SD16×D1311yescharacteristic
795C23#8816811yescharacteristic
796C23#8816911yescharacteristic
797C23#8817011yescharacteristic
798C23Q16×D1311yescharacteristic
799C23#8817211yescharacteristic
800C23#8817211yescharacteristic
801C23#8817311yescharacteristic
802C23#8819111yescharacteristic
803C23#8819111yescharacteristic
804C23#8819211yescharacteristic
805Q8—24no—
806Q8—24no—
807Q8—42no—
808Q8—42no—
809Q8—42no—
810Q8—42no—
811Q8—42no—
812Q8—42no—
813C2×C4—24no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—81no—
824C2×C4—81no—
825C2×C4—81no—
826C2×C4—81no—
827C2×C4—264no—
828C2×C4—262no—
829C2×C4—262no—
830C2×C4—262no—
831C2×C4—522no—
832C2×C4—522no—
833C2×C4—522no—
834C2×C4—522no—
835C2×C4—522no—
836C2×C4—522no—
837C2×C4—521no—
838C2×C4—521no—
839C2×C4—521no—
840C2×C4—521no—
841C2×C4—522no—
842C2×C4—522no—
843C2×C4—522no—
844C2×C4—522no—
845C2×C4—522no—
846C2×C4—522no—
847C2×C4—522no—
848C2×C4—522no—
849C2×C4—522no—
850C2×C4—522no—
851C2×C4—522no—
852C2×C4—1041no—
853C2×C4—1041no—
854C2×C4—1041no—
855C2×C4—1041no—
856C2×C4C22⋊C4×D1311yescharacteristic
857C2×C4#8813511yescharacteristic
858C2×C4#8813511yescharacteristic
859C2×C4#8813611yescharacteristic
860C2×C4#8813611yescharacteristic
861C2×C4#8813711yescharacteristic
862C2×C4#8813811yescharacteristic
863C2×C4#8813811yescharacteristic
864C2×C4#8813811yescharacteristic
865C2×C4#8813911yescharacteristic
866C2×C4#8813911yescharacteristic
867C2×C4#8814011yescharacteristic
868C2×C4C2×#610311yescharacteristic
869C2×C4C4×C22⋊D1311yescharacteristic
870C2×C4C4×C22⋊D1311yescharacteristic
871C2×C4#8818311yescharacteristic
872C2×C4#8818411yescharacteristic
873C2×C4#8818411yescharacteristic
874C2×C4#8819111yescharacteristic
875C2×C4#8819111yescharacteristic
876C2×C4#8819211yescharacteristic
877C2×C4#8819311yescharacteristic
878C2×C4#8819311yescharacteristic
879C2×C4#8819311yescharacteristic
880C2×C4#8819311yescharacteristic
881C2×C4#8819411yescharacteristic
882C2×C4#8819411yescharacteristic
883C2×C4#8820711yescharacteristic
884C8—42no—
885C8—522no—
886C22—264no—
887C22—264no—
888C22—264no—
889C22—522no—
890C22—522no—
891C22—522no—
892C22—522no—
893C22—522no—
894C22—522no—
895C22—522no—
896C22—522no—
897C22—522no—
898C22—522no—
899C22—522no—
900C22—522no—
901C22D13×#10311yescharacteristic
902C22#1171846311yescharacteristic
903C22#1171846411yescharacteristic
904C22#1171846511yescharacteristic
905C22#1171846611yescharacteristic
906C22#1171846711yescharacteristic
907C22#1171846811yescharacteristic
908C22#1171846911yescharacteristic
909C22#1171847011yescharacteristic
910C22#1171847111yescharacteristic
911C22#1171847211yescharacteristic
912C22#1171847311yescharacteristic
913C22#1171847411yescharacteristic
914C22#1171847511yescharacteristic
915C22#1171847611yescharacteristic
916C22#1171847711yescharacteristic
917C22#1171861611yescharacteristic
918C22#1171861711yescharacteristic
919C22#1171861711yescharacteristic
920C22#1171862011yescharacteristic
921C22#1171862111yescharacteristic
922C22#1171862211yescharacteristic
923C22#1171883011yescharacteristic
924C22#1171883111yescharacteristic
925C22#1171883211yescharacteristic
926C22#1171883311yescharacteristic
927C22#1171883411yescharacteristic
928C22#1171883511yescharacteristic
929C22#1171884711yescharacteristic
930C22#1171884711yescharacteristic
931C22#1171884811yescharacteristic
932C22#1171884811yescharacteristic
933C22#1171884911yescharacteristic
934C22#1171885011yescharacteristic
935C22#1171888411yescharacteristic
936C4—44no—
937C4—82no—
938C4—524no—
939C4—522no—
940C4—1042no—
941C4#1171861811yescharacteristic
942C4#1171861811yescharacteristic
943C4#1171861911yescharacteristic
944C4#1171862011yescharacteristic
945C4#1171862111yescharacteristic
946C4#1171862211yescharacteristic
947C4#1171887411yescharacteristic
948C4#1171888411yescharacteristic
949C2—524no—
950C2#1311307511yescharacteristic
951C2#1311476911yescharacteristic
952C2#1311477511yescharacteristic
953C2#1311514011yescharacteristic
954C2#1311514511yescharacteristic
955C2#1311525611yescharacteristic
956C2#1311526611yescharacteristic
957C2#1311583611yescharacteristic
958C2#1311583811yescharacteristic
959C2#1311584311yescharacteristic
960C2#1311584511yescharacteristic
961C2#1311603011yescharacteristic
962C2#1311603111yescharacteristic
963C2#1311603711yescharacteristic
964C2#1311603811yescharacteristic
subgroupG/H
centerC24D4×D13
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC22×C13×#103C2
socleC24×C13C2×D4
prime radicalC24×D13D4
cosocleC23×C4×C13C23
hypercenterC22×#103D13
hypocenterC13#10970
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#103

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C22×#88075C2semidirect
5. C2×#11718143C2semidirect
6. C2×#11718121C2semidirect
7. C22×C13×#103C2semidirect
17. C2×#88200C4semidirect
166. C2×Q8×C13C22⋊C4semidirect
264. C4⋊Dic13C22⋊C4semidirect
275. C22×#103D13semidirect
329. C22×D13#103semidirect
647. C2×Q8#6103semidirect
754. C13#10970semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#882002
C22×#880752
C22×#880602
C2×#117186482
C2×#117181432
C2×#117181212
C22×C13×#1032
#1097013